(1) Field of the Invention
The present invention relates generally to the scientific field of optimal estimation, and more particularly, relates to a model assessment system and method used in the area of contact tracking or target motion analysis that is based on fuzzy logic inferencing methods.
(2) Description of the Prior Art
Expert systems can be used to identify likely models of physical phenomena in response to information about the state of the phenomena. One type of physical phenomena that can be modeled is the motion of a signal source moving in a medium where the signal propagated through the medium is corrupted by noise.
In an underwater environment, for example, localization and tracking of an acoustic contact from sonar measurements are of considerable interest. Several estimation techniques have been applied to the tracking problem with varying results. The differences in techniques involve (1) the modeling of the process, and (2) the selection and formulation of the estimation algorithm. Sources of uncertainty in the modeling process include assumptions on contact kinematics, acoustic propagation mechanisms and measurement noise characteristics. Understanding and conveying the impact of these uncertainties on overall system performance is a critical issue. Model assessment is a crucial phase of contact tracking, leading to an appraisal of the system performance in the presence of modeling uncertainties. Model assessment involves identification of features from measurement residuals for formulation of possible causes of mismodeling associated with the system models employed in the tracking process.
A hierarchical approach to filtering and estimation for contact tracking was first proposed by A. G. Lindgren, et al., xe2x80x9cNonlinear Parameter Estimation With Segmented Data: Trajectory Estimation With Biased Measurementsxe2x80x9d, Proceedings of the 19th IEEE Asilomar Conference on Signals, Systems and Computers, pp. 349-353, November, 1985, incorporated herein by reference, and has been developed for generation of a tactical picture, as disclosed by K. F. Gong et al., xe2x80x9cIntelligent Data Integration for Tactical Picture Generation: Performance Analysis of Advanced Techniquesxe2x80x9d, TTCP Subgroup G Symposium on Shallow Water Undersea Warfare, Nova Scotia, October, 1996, incorporated herein by reference. The hierarchical model of intelligent data integration for generation of the tactical picture is shown generally in FIG. 1. This process entails (1) data conditioning, which associates and characterizes available data, and provides uncertainty descriptions; (2) data processing, which processes the conditioned data to form and maintain contact tracks, propagates the uncertainties, and provides for uncertainty descriptions associated with the resulting tracks; (3) model assessment, which detects, interprets and resolves anomalies due to uncertainties in modeling assumptions; and (4) the process controller, which provides for scenario driven adaptive processing by appropriate selection of data, models and algorithms.
Conventional approaches for propagation of uncertainty in contract tracking have primarily focused on probabilistic techniques, as disclosed by V. J. Aidala, xe2x80x9cKalman Filter Behavior in Bearings-Only Tracking Applicationsxe2x80x9d, IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-15, No. 1, pp. 29-39, January, 1979, incorporated herein by reference. In particular, Bayesian methods have been used. The quality of the estimated track is evaluated based on a priori knowledge of statistical uncertainties associated with the sensor measurements and the process model, i.e., input and modeling uncertainties. These uncertainties are typically represented as additive white Gaussian noise and are propagated through the conditional covariance matrix to form containment regions that indicate the final uncertainty associated with the contact state estimate, as described in S. C. Nardone et al., xe2x80x9cFundamental Properties and Performance of Conventional Bearings-Only Target Motion Analysisxe2x80x9d, IEEE Transactions on Automatic Control, Vol. AC-29, No. 9, pp. 775-787, September, 1984, incorporated herein by reference. Mismodeling in the tracking process has a severe impact on the integrity of the estimate and the uncertainties associated with those estimates. This includes erroneous assumptions, such as constant contact velocity, known acoustic propagation path and Gaussian noise distributions, as well as erroneous model-order approximation.
To alleviate these difficulties in modeling, a contact management model assessment algorithm using the Dempster-Shafer approach has been developed, as disclosed in U.S. Pat. No. 5,581,490 issued to Ferkinhoff et al., and incorporated herein by reference. The Dempster-Shafer Theory of Evidential Reasoning represents a generalization of Bayesian probability for producing inferences from uncertain information. The results using this approach, however, can be inconclusive if there is a high degree of conflict in the evidence.
It is therefore an object of the invention to provide a model assessment system and method for contact tracking that uses fuzzy logic.
The present invention features a fuzzy logic based model assessment system for assessing at least one model of physical phenomena using measurement residual values representing a difference between a measured data sequence corresponding to the physical phenomena and an expected data sequence corresponding to the model to be assessed. The system comprises a feature identification module that identifies one or more features present in the measurement residual values and generates one or more feature amplitude values and feature amplitude standard deviation values. The system also comprises an anomaly characterization module that characterizes the features in one or more membership classes based upon the feature amplitude value and generates class membership interval values for each membership class based upon the feature amplitude standard deviation value. The class membership interval values represent a range of degrees of membership in each of the membership classes. The system further comprises a hypothesis formulation and evaluation module for determining at least one mismodeling hypothesis by applying fuzzy inferencing to the class memberships, and generates at least one hypothesis certainty interval value representing a range of degree of certainty of the mismodeling hypothesis.
According to one example, the physical phenomena includes a moving contact, the model is a contact tracking model, and the one or more features include one or more tracking anomalies. Examples of the tracking anomalies include a jump feature representing a discontinuity in a measured tracking signal and a drift feature representing a generally-linear drift of the measured tracking signal. Examples of the membership classes include null, weak, moderate and strong. The class membership interval values preferably include an upper limit value representing the greatest possible extent to which the feature belongs to the membership class and includes a lower limit value representing the smallest necessary extent to which the feature belongs to the membership class. The hypothesis certainty value also preferably includes hypothesis certainty interval values representing a range of certainty for the mismodeling hypotheses.
According to one embodiment, the hypothesis formulation and evaluation module includes a knowledge base and an inferencing module. The knowledge base includes a plurality of rules for inferring one or more mismodeling hypotheses based upon features and their corresponding membership classes. The inferencing module applies one or more rules from the knowledge base to the class memberships, selects one or more mismodeling hypotheses based upon the rule, and generates hypothesis certainty interval values representing a range of certainty for the selected mismodeling hypothesis based on the class membership interval values. The hypothesis formulation and evaluation module can also include an aggregation module. Where the inferencing module applies a plurality of rules that results in the same mismodeling hypothesis with different hypothesis certainty interval values, the aggregation module aggregates the hypothesis certainty interval values to generate a composite hypothesis certainty interval value for the mismodeling hypothesis.
The present invention also features a fuzzy inference system for use with a model assessment system comprising the anomaly characterization module and the hypothesis formulation and evaluation module as described above. According to one embodiment, the feature identification module, anomaly characterization module, and hypothesis formulation and evaluation module are implemented on a computer.
The present invention also features a method of assessing one or more models of physical phenomena in response to a measured data sequence representing a signal caused by the physical phenomena in the presence of noise. The method comprises providing measurement residual values representing a difference between the measured data sequence and an expected data sequence corresponding to the model to be assessed. One or more features are then identified in the measurement residual values, and one or more feature amplitude values and feature amplitude standard deviation values are generated for the identified feature. The feature is then characterized in one or more membership classes based upon the feature amplitude value, and class membership interval values are generated for each of the membership classes based upon the feature amplitude standard deviation value. One or more mismodeling hypotheses are then determined by applying fuzzy inferencing to the class memberships and one or more hypotheses certainty interval values are generated, representing a degree of certainty of the mismodeling hypothesis. The method can also include the step of using the mismodeling hypothesis and the hypothesis certainty values to assess the model and generate a tactical picture.